General Form of the Theorem on Equivalent Ratios

Q.

The ratio of third proportional to $12$ and $30$ and the mean proportional between $9$ and $25$ is

Q. If x is a positive number and the geometric mean of 9 and 16, find the value of x?

1. 3
2. 4
3. 25
4. 12

Q.

Find the mean proportional between the following:

$5$ and $20$

Q.

Find the mean proportion between $3$ and $12.$

Q.

If $p,q,r,s$are in proportion, then we have

1. $p:q::r:s$

2. $p:s::q:r$

3. $Both\left(a\right)and\left(b\right)$

4. $q:r::p:s$

Q.

Find the mean proportional between the following:

$2$ and $18$

Q.

Are the following numbers in proportion?

$5,6,20,18$

Q.

Find the mean proportional between 0.3 and 2.7

1. 0.03

2. 0.9

3. 0.09

4. 0.81

Q.

In a proportion the second and third term are called …………………… . [ extremes / means ]

Q.

Find the mean proportional between $48$ and $75$.

Q.

Find the mean proportional between the following:

$3$ and $12$

Q.

Find the mean proportional between $3$ and $12$.

Q.

What should be added to each of the numbers $13,17$ and $22$ so that, the resulting numbers are in continued proportion?

1. $4$

2. $5$

3. $6$

4. $3$

Q.

Are the following numbers in proportion?

$30,45,16,32$

Q.

If $\frac{1}{5}:\frac{1}{x}=\frac{1}{x}:\frac{1}{1.25}$, then the value of x is

1. 5

2. 2.5

3. 5.2

4. 2

Q. 7 is the mean proportion between two numbers x and y and 56 is third proportion to x and y. Find the numbers.
$\left[3\right]$

Q.

The mean proportional between 2.5 and 10 is ____

1. 4

2. 2.5

3. 5

4. 3.5

Q.

7 is the mean proportion between two numbers x and y and 56 is third proportion to x and y. Find the numbers.

1. x = 2.5, y = 16

2. x = 3.5, y = 14

3. x = 1.5, y = 12

4. x = 4, y = 14

Q. What should be added to each of the numbers $13,17$ and $22$ so that, the resulting numbers are in continued proportion?
[3 Marks]

Q.

If $9,x,x$ and $49$ are in proportion, find the value of $x$.

1. $7$

2. $14$

3. $21$

4. $35$

Q. If x, y and z are in continued proportion then $z:x::z^2:$.

1. $x^2$
2. $y^2$
3. $y$

Q.

Are the following numbers in proportion?

$30,40,45,60$

Q.

Determine if the following is in proportion.

$34,48,70,120$

Q. If a : b = c : d, then according to dividendo property

1. a-b:a=c-d:c
2. a+b:b=c+d:d
3. a+b:a=c+d:c
4. a-b:b=c-d:d

Q. If a : b = c : d, then according to componendo property

1. a+b:b=c+d:d
2. a-b:a=c-d:c
3. a+b:a=c+d:c
4. a-b:b=c-d:d

Q.

Are the following numbers in proportion?

$8,9,80,100$

Q.

Are the following numbers in proportion?

$13,27,39,81$